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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th13</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: NUMBER16:13</font></span><br/></a><div class="add">(  <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>, <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> 12 <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 8 &amp;  <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> 1, <a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <span class="p1">(<span class="default">12 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> 8 &amp; (  for <font color="Olive" title="b1">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 12 holds <br/>( <span class="p1">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 &amp; <span class="p1">(<span class="default"><a href="pre_ff.html#K2" title="PRE_FF:func.2">Fib</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 8 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 6 ) ) )</div></div>
